Consider the standard overlapping generations economy in which fiat money is the only asset. Each period, 10,000 young people are born. The initial old hold fiat money and the aggregate quantity is $1,000,000. We assume that the fiat money stock increases over time, following the rule 1 1.25 M M t t = . Each period, the newly printed money is given to old people. Each young person is endowed with 10,000 units of the consumption good. Each young person saves 4,000 goods regardless of the return on money. a. Write down the budget constraint for a young person, for an old person, and then derive the lifetime budget constraint. b. In one sentence, explain how you would compute the gross real return for money. Solve for the stationary equilibrium gross real return in this economy. c. Write down the government budget constraint. Be sure to give a definition of each variable that is present in this budget constraint. (In other words, define each term in the expression.) d. Solve the subsidy that each old person will receive in this economy. e. Solve for the equilibrium price level in period 1, 1 p , in this economy